Neither the existence of a global tendency toward the centralization of capital as theorized by Marx nor the possible links between economic crisis and capital centralization have been verified by empirical studies. Using techniques of complex network analysis applied to the Thomson Reuters Eikon database we introduce a definition of centralization as network control and present a first study of its global evolution from 2001 to 2016. We find that the global network control is highly centralized: the fraction of the top holders cumulatively holding the 80% of the global economic value of the companies examined does never exceed 2%. Furthermore, by inspecting the temporal dynamics of the phenomenon we observe a relevant increase in the centralization of capital: this trend assumes a more regular and general character since the financial crisis started in 2007, with a growth of more than 20%.